Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Find a Function Value Example 2:Make a Function Table Example 3:Real-World Example: Independent and Dependent Variables Example 4:Real-World Example: Analyze Domain and Range Example 5:Real-World Example: Write and Evaluate a Function Five-Minute Check

Main Idea/Vocabulary Complete function tables. function function table independent variable dependent variable

NGSSS MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range, and the difference between discrete and continuous data. MA.8.A.1.5 Translate among verbal, tabular, graphical, and algebraic representations of linear functions.

Example 1 Find a Function Value Find f(–6) if f(x) = 3x + 4. f(x)=3x + 4 Write the function. f(–6)=3(–6) + 4 Substitute –6 for x into the function rule. f(–6)=– or –14 Simplify. Answer: So, f(–6) = –14.

Example 1 CYP Find f(–2) if f(x) = 4x + 5. A.–13 B.–3 C.3 D.13

Example 2 Choose four values for x to make a function table for f(x) = 4x – 1. Then state the domain and range of the function. Substitute each domain value x into the function rule. Then simplify to find the range value. Make a Function Table Answer: The domain is {–2, –1, 0, 1}. The range is {–9, –5, –1, 3}.

Example 2 CYP Use the values –2, –1, 0, 1 for x to make a function table for f(x) = 2x + 3. State the domain and range of the function. A.domain: {−2, −1, 1} range: {0, 1, 3, 5} B.domain: {–2, –1, 0, 1} range: {–1, 1, 3, 5} C.domain: {–2, –1, 0, 1} range: {1, 3, 5} D.domain: {–1, 1, 3, 5} range: {–2, –1, 0, 1}

Example 3 FOOD Linda buys a can of tuna fish that weighs 4.2 ounces. The total weight w of any number of cans c of tuna fish can be represented by the function w(c) = 4.2c. Identify the independent and dependent variables. Independent and Dependent Variables Answer: Since the total weight of the cans depends on the number of cans, the total weight w is the dependent variable and the number of cans c is the independent variable.

Example 3 CYP FOOD There are approximately 275 miniature marshmallows in a 10.5-ounce bag of marshmallows. The total number of marshmallows m in any number of bags b can be represented by the function m(b) = 275b. Identify the independent and dependent variables. A.The number of marshmallows m is the dependent variable. The number of bags b is the independent variable. B.The number of bags b is the dependent variable. The number of marshmallows m is the independent variable.

Example 4 FOOD Linda buys a can of tuna fish that weighs 4.2 ounces. The total weight w of any number of cans c of tuna fish can be represented by the function w(c) = 4.2c. What values of the domain and range make sense for this situation? Explain. Analyze Domain and Range Answer: Only whole numbers make sense for the domain because you cannot buy a fraction of a can of tuna fish. The range values depend on the domain values, so the range will be rational number multiples of 4.2.

Example 4 CYP FOOD There are approximately 275 miniature marshmallows in a 10.5-ounce bag of marshmallows. The total number of marshmallows m in any number of bags b can be represented by the function m(b) = 275b. What values of the domain and range make sense for this situation? Explain. A.Only positive rational numbers make sense for the domain. The range will be multiples of 275. B.Only whole numbers make sense for the domain. The range will be multiples of C.Only whole numbers make sense for the domain. The range will be multiples of 275. D.The domain will be multiples of 275. The range will be whole numbers.

Example 5 DANCE A dance studio charges an initial fee of $75 plus $8 per lesson. Write a function to represent the cost c(ℓ) for ℓ lessons. Then determine the cost for 13 lessons. Write and Evaluate a Function The function c(ℓ) = 8ℓ + 75 represents the situation.

Example 5 To find the cost for 13 lessons, substitute 13 for ℓ. Answer: It will cost $179 for 13 lessons. Write and Evaluate a Function c(ℓ)=8ℓ + 75Write the function. c(ℓ)=8(13) + 75 or 179Substitute 13 for ℓ.

Example 5 CYP PHOTOGRAPHY A photographer charges a $55 sitting fee plus $15 for each pose. Write a function to represent the cost c(p) for p poses. Then determine the cost for 8 poses. A.c(p) = 55c + 15; $455 B.c(p) = 15c + 55; $175 C.c(p) = 55p + 15; $455 D.c(p) = 15p + 55; $175

Find f(3) if f(x) = x Five Minute Check 1 A.12 B.14 C.15 D.16

Find f(5) if f(x) = 4x. Five Minute Check 2 A.9 B.20 C.24 D.25

Find f(6) if f(x) = 2x – 1. Five Minute Check 3 A.11 B.12 C.13 D.15

Find f(–7) if f(x) = –3x + 2. Five Minute Check 4 A.–23 B.–21 C.21 D.23

Elizabeth is buying candles. They are $5.43 a piece. She is not sure how many she wants to buy. Write a function to calculate the total cost for any given number of candles c. Five Minute Check 5 A.f(c) = 5.43c B.f(c) = c C.f(c) = 5.43 – c D.

Which function represents the rule shown in the function table? Five Minute Check 6 A.y = x + 45 B.y = 3x C.y = 3x + 4 D.y = 2x + 3